Sep. 10, 2008Kentarou Mawatari Taiwan1/30 Azimuthal angle correlation in VBF processes at LHC arXiv:0809.XXXX Mawatari, Kentarou 馬渡健太郎 마와타리 켄타로.

Sep. 10, 2008 Kentarou Mawatari (KIAS) @ Taiwan 1/30

Azimuthal angle Azimuthal angle correlation correlation

in VBF processes at in VBF processes at LHCLHC

arXiv:0809.XXXXMawatari, Kentarou

馬渡　健太郎마와타리 켄타로

with K.Hagiwara (KEK) and Q.Li (Karlsruhe)

Heidelberg U.


Contents Introduction

Azimuthal correlations in H+2jet events Formalism and Kinematics Helicity amplitudes for the VBF process Azimuthal angle correlations

Higgs bosons Massive gravitons

Summary


Introduction


Motivation I: the Higgs properties After observation of a Higgs boson at LHC,

determination of its properties, i.e., all the couplings and quantum numbers, is the next goal to unravel the underlying theory. the gauge, Yukawa, and self-couplings the charge, color, spin, CP quantum numbers

Spin & CP properties at LHC Higgs decay, e.g. H->ZZ->(ll)(ll) Higgs+2jet production, pp->Hjj

Dell’Aquila,Nelson(1986)S.Y.Choi et al.(2003)Buszello et al.(2004)T.Plehn et al.(2002)


Higgs production at LHCA.Djouadihep-ph/0503172

WBF


Azimuthal angle correlations in WBF The anomalous HWW

couplings

The azimuthal correlations reflects the tensor structure of the Higgs couplings.

Why is SM flat ? Why is CP-even (odd) suppressed at phi=90 (0 and 180) ?

T.Plehn, D.Rainwater, D.ZeppenfeldPRL88(2002)051801


H+2 jet events are produced also via gluon fusion (GF);(a) qq>qqH, (b) qg>qgH, (c) gg>ggH.

WBF vs. GF V. Del Duca et al.NPB616(2001)367

w/ minimal cuts

• minimal cuts:


The distinctive kinematics of WBF

Far forward and backward jets.

The Higgs boson is produced centrally.

the t-channel weak-boson propagator

D.Rainwaterhep-ph/0702124


Minimal cuts: VBF cuts:

WBF vs. GF with VBF cutsV. Del Duca et al.NPB616(2001)367

w/ minimal and VBF cutsw/ minimal cuts


WBF vs. GF in the az dis. Why is GF suppressed at phi=90 ?

This reflects the effective Hgg coupling .

The VBF cuts may select the t-channel VBF diagrams.

The t-channel vector-boson propagators lead to the distinctive far forward jets. The kinematical feature is not

particular only to WBF but also the QCD production via the t-channel GF processes.

V. Del Duca et al.NPB616(2001)367

w/ minimal and VBF cuts


Parton-shower effect

The present consensus seems to be that the azimuthal angle correlations predicted in the leading-order may survive even after higher-order corrections are applied.

The following analyses are done at the parton level with tree level matrix elements.

V. Del Duca et al.JHEP0610(2006)016


Motivation II: massive gravitons As another interest to study the azimuthal correlations at

LHC, we attempt to apply it to other heavy particle productions, here massive-graviton productions.

We consider the simplest Randall-Sundrum (RS) model, where only gravitons can propagate in extra dimension.

So far, several phenomenological studies have been made on the s-channel graviton resonances and their decays for the discovery and the determination of the spin-2 nature. Davoudiasl et al. (2000,2001)

Allanach et al. (2000,2002), Traczyk, Wrochna (2002)Abazov et al. [D0 collaboration] (2005)

We study the massive-graviton production via the VBF process, which may have a potential to determine its properties as in the Higgs case.


Formalism and Kinematics

Helicity amplitude formalism Kinematics


Helicity formalism For the VBF process

the completeness relation for space-like vector-boson

the conserved current


X decay to a vector-boson pair


Kinematics


Helicity amplitudesfor the VBF process

Fermion current amplitudes Gluon current amplitudes Off-shell VBF amplitudes


Off-shell vector-boson Current amplitudes For the production

Fermion currents:

Gluon currents:


Fermion current amplitudes


Gluon current amplitudes


XVV vertex Off-shell VBF amplitudes

The XVV vertex

The polarization tensor and the GXX vertices

For , where the VBF contributions dominant, WBF Higgs bosons --- produced by the longitudinally

polarized weak-bosons. Loop-induced Higgs bosons --- produced by the

transversely polarized vector-bosons. Sep. 10, 2008 Kentarou Mawatari (KIAS) @ Taiwan 22/30

VBF amplitudes for Higgs bosons

For , the λX=±2 states are dominantly produced through the collisions of the vector-bosons which have the opposite-sign transverse polarization.


VBF amplitudes for gravitons


Dijet large rapidity separation Minimal cuts: VBF cuts:

As the large rapidity separation cuts are imposed, the VBF contributions tend to dominate the exact matrix elements.


Azimuthal angle correlations Higgs bosons Massive gravitons


Quantum interferencebetween the different helicity states The VBF helicity amplitude for Higgs bosons (λX=0)

Using the relative phases

Azimuthal correlations H(WBF): H(GF): A:


Azimuthal correlation of Higgs bosons

The VBF contributions can reproduce the distributions with the exact matrix elements very well not only for WBF but also GF.

• minimal cuts:• VBF cuts:


Azimuthal correlation of massive-gravitons

The full helicity amplitude for massive-gravitons The λX=±2 caes is dominant.

There is no interference term. No azimuthal dependence.

"Graviton production with 2 jets at the LHC in large extra dimensions" K.Hagiwara, P.Konar, Q.Li, K.M., D.Zeppenfeld [JHEP0804,019]

"HELAS and MadGraph/MadEvent with spin-2 particles" K.Hagiwara, J.Kanzaki, Q.Li, K.M. [appear in EPJ, arXiv:0805.2554]




Summary We have studied heavy-particle (Higgs boson and massive-

graviton) productions in association with two jets via VBF (=WBF+GF) and their decays at LHC.

We showed the helicity amp explicitly for the VBF subprocesses. the VBF amp reproduces the exact matrix elements by

taking into account the dijet large rapidity separation. quantum interference between different helicity states

of the intermediate vector-bosons leads to a non-trivial azimuthal angle correlation of the jets in the production and in the decay.

These correlations reflect the spin and CP nature of the heavy particles produced via VBF processes.


Supplements


Relation to the splitting amplitudes For the production

z: the energy fraction of the initial parton that is carried off by the space-like vector-boson

For the decay z’: the energy fraction of the time-like vector-

boson that is carried off by the final parton

the collinear limit

the collinear limit


(unregularized) splitting functions


Gluon current amplitudes


Kinematical cuts Minimal cuts: VBF cuts:

Additional pT cut:



Sep. 10, 2008Kentarou Mawatari Taiwan1/30 Azimuthal angle correlation in VBF processes at LHC arXiv:0809.XXXX Mawatari, Kentarou 馬渡 健太郎 마와타리 켄타로.

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Sep. 10, 2008Kentarou Mawatari Taiwan1/30 Azimuthal angle correlation in VBF processes at LHC arXiv:0809.XXXX Mawatari, Kentarou 馬渡健太郎 마와타리 켄타로.